Fremont police shot and killed a naked man with a knife after he refused to drop the weapon while chasing his estranged wife, authorities said Monday.

The name of the slain suspect, a 37-year-old San Jose man, was not released.

The incident began about 11 p.m. Sunday when a woman called police to report that her roommate was being attacked by the roommate's estranged husband at their apartment on the 4500 block of Central Avenue, said Geneva Bosques, a spokeswoman for the Fremont Police Department.

As two officers arrived, they saw the roommate running from the apartment while being chased by a naked man with a knife, Bosques said.

The officers demanded that the suspect drop the knife, but he refused, prompting them to open fire, Bosques said.

The man died at a local hospital.

One of the officers involved in the shooting has been with the department for three years while the other has served for more than 20 years, police said.

Their names were not released. They were placed on paid administrative leave, which is routine, pending investigations by police and the Alameda County district attorney's office.